The electric current in a charging R-C circuit is given by where R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.

Draw a graph from the following data. Draw tangents at x = 2, 4, 6 and 8. Find the slopes of these tangents. Verify that the curve drawn is y = 2x² and the slope of tangent is

x 1 2 3 4 5 6 7 8 9 10

y 2 8 18 32 50 72 98 128 162 200

A curve is represented by y = sin x. If x is changed from to find approximately the change in y.

The electric current in a discharging R-C circuit is given by where R and C are constant parameters and t is time. Let i₀ = 2.00 A, R = 6.00 × 10⁵ Ω and C = 0.500 μF. (a) Find the current at t = 0.3 s. (b) Find the rate of change of current at t = 0.3 s. (c) Find approximately the current at t = 0.31 s.

Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.